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MASH : Maths and Stats Help

Wilcoxon Signed Ranks Test



A Wilcoxon test, sometimes called a Wilcoxon Signed-Rank Test, compares the means between two related groups, such as comparing the difference between pre-intervention and post-intervention test results.

It is considered a non-parametric test and therefore it is suitable for non-parametric data. To check if your data is parametric, please check our dedicated guide: Parametric or Not Guide (PDF)

If your data is parametric you should consider using a Paired-Samples t-Test


Test Procedure


  1. Click Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples

  2. Within the ‘Two Related Samples Tests’ box, select the two variables you wish to analyse and move to them to the ‘Test Pairs’ box using the right arrow

  3. Select Options and click on the Descriptives and the Quartiles

  4. Click "Continue" then "OK".



SPSS will generate three tables, for this test we need all three, the Descriptive Statistics, the Wilcoxon Signed Ranks Test and the Test Statistics.


Descriptive Statistics

This table shows a selection of descriptive statistics: the sample size of each group (N), the mean of each group (Mean), the standard deviation of each group (Std. Deviation), and the median of each group (50th Median) best practice is to report them all.

Wilcoxon Signed Ranks Test

From this table we can calculate our Wilcoxon Statistics (W) this is the lower of the two (Sum of Ranks)

Test Statistics

This table shows the specific test results including the z score (Z) and the p-value/significance value (Asymp. Sig. (2-tailed))

Reporting the Results in APA Formatting

Students’ test results were compared before and after the intervention workshop. On average, students performed better (Mdn = 73.00) after the intervention than before (Mdn = 72.00). A Wilcoxon Test indicated this improvement, was statistically significant, W = 2858, z = 2.02, p = .043.